Order recursive computation for a MIMO equalizer

ABSTRACT

A receiver module includes an input that receives a data message from a wireless communication channel. The data message has a plurality of training fields and data. A channel estimator module recursively estimates a matrix H that represents the channel based on the plurality of training fields. The recursive estimation is performed as the plurality of training fields are being received. An equalizer module applies coefficients to the data based on the matrix H.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/759,453, filed on Jan. 17, 2006. The disclosure of the aboveapplication is incorporated herein by reference in its entirety.

FIELD

The present disclosure relates to channel estimation in a wirelesscommunication system.

BACKGROUND

The Background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description which may nototherwise qualify as prior art at the time of filing, are neitherexpressly or impliedly admitted as prior art against the presentdisclosure.

Some multiple input, multiple output (MIMO) wireless communicationsystems can estimate channel conditions, or gains, in the communicationpath between the transmitting and receiving antennas. The channelestimation process can include transmitting known training symbols,receiving the known training symbols, and processing the receivedsymbols to estimate the channel conditions. The estimation is based ondifferences between the known training symbols and the received symbols.Information regarding the channel conditions can then be used to programcoefficients of an equalizer of the receiver. The equalizer thencompensates for the channel conditions.

Referring now to FIG. 1, an example is shown of a MIMO communicationsystem 10 that complies with the Institute of Electrical and ElectronicsEngineers (IEEE) 802.11n specification, which is hereby incorporated byreference in its entirety. A transmitter module 12 communicates with areceiver module 14 via a wireless communication channel 16. A matrix Hrepresents signal gains through channel 16.

Transmitter module 12 periodically generates a plurality of longtraining fields (LTFs) 18-1, . . . , 18-j, referred to collectively asLTFs 18. Each LTF 18 includes a plurality of training symbols 20-1, . .. , 20-k, referred to collectively as training symbols 20. A multipliermodule 22 multiplies each training symbol 20 by a corresponding columnof a preamble steering matrix P. A number of rows n of matrix Pcorresponds with a number of transmit antennas 26-1, . . . , 26-n,collectively referred to as antennas 26. The number of columns j ofmatrix P corresponds with the number of LTFs 18. Matrix P assures theorthogonality of training symbols 20 as they are transmitted fromantennas 26. Matrix P has a condition number of 1, i.e. cond(P)=1.

Receiver module 14 includes receiver antennas 30-1, . . . , 30-n,collectively referred to as antennas 30, that receive the trainingsymbols via channel 16. After receiving all of the training symbols,receiver module 14 generates matrix H based on known training symbols20, matrix P, and the received training symbols. Receiver module 14 canthen use matrix H to adjust coefficients of an internal equalizationmodule for signals from antennas 30. It is generally desirable forreceiver module 14 to generate matrix H as quickly as possible.

A sample estimation of matrix H will now be described. Assume that n=3and j=4. Transmitter module 12 then sends 4 LTFs 18 and matrix P is a3×4 matrix

$P = {\begin{bmatrix}1 & {- 1} & 1 & 1 \\1 & 1 & {- 1} & 1 \\1 & 1 & 1 & {- 1} \\{- 1} & 1 & 1 & 1\end{bmatrix}.}$

The effective MIMO channel estimated at receiver module 14 is given byH_(est)=HP

H=H_(est)P⁻¹, where H_(est) represents an estimation of matrix H. Forthe data associated with each LTF 18 the transmitter-to-receivercommunication model can be described by y=H_(est)P⁻¹x+n, where xrepresents transmitted data symbols. The ZF solution is applied to thematrix H_(est)P⁻¹.

If the matrix P were not used, y=Hx+n

{circumflex over (x)}=R⁻¹Q*y, where y represents received data symbols.With matrix P, y=H_(est)P⁻¹x+n. Receiver module 14 uses each LTF 18 toestimate a column of matrix H_(est). Matrix H can therefore be estimatedby waiting until all columns have been estimated and then estimating thematrix H_(est)P⁻¹. Receiver module 14 can then performorthogonal-triangular decomposition (QR) on H_(est)P⁻¹, i.eQR(H_(est)P⁻¹). However, the computational density increases to theorder of n³, i.e. O(n³). To meet the processing latency the hardwareburden would also increase based on O(n³).

The effect of matrix P will now be described to shed light on the aboveequations. Let H_(est)=QR. Without matrix P the equalized vector isgiven by

${\hat{x} = {\frac{1}{{diag}\left( {R^{- 1}R^{-^{*}}} \right)}R^{- 1}Q^{*}y}},{{{where}\mspace{14mu} W_{}} = {\frac{1}{{diag}\left( {R^{- 1}R^{-^{*}}} \right)}.}}$

With matrix P the equalized vector is given by:

${\hat{x} = {\frac{1}{{diag}\left( {\left( {RP}^{- 1} \right)^{- 1}\left( {RP}^{- 1} \right)^{-^{*}}} \right)}{PR}^{- 1}Q^{*}y}},{where}$$W_{} = {\frac{1}{{diag}\left( {\left( {RP}^{- 1} \right)^{- 1}\left( {RP}^{- 1} \right)^{-^{*}}} \right)}.}$

The equivalent matrix RP⁻¹ is a full matrix and it is difficult tocompute its inverse for an n×n communication system. SUMMARY

A receiver module includes an input that receives a data message from awireless communication channel. The data message has a plurality oftraining fields and data. A channel estimator module recursivelyestimates a matrix H that represents the channel based on the pluralityof training fields. The recursive estimation is performed as theplurality of training fields are being received. An equalizer moduleapplies coefficients to the data based on the matrix H.

In other features the channel estimator module begins the recursiveestimation upon receiving a first one of the training fields andfinishes the recursive estimation upon receiving a final one of theplurality of training fields. The channel estimator module estimates thematrix H based on a matrix P. the plurality of training symbols areprocessed in accordance with the matrix P prior to being transmitted tothe receiver module. The recursive estimation of matrix H includesrecursively estimating a matrix H_(est) based on the plurality oftraining fields and estimating matrix H based on an inverse of matrix Pand a final value of the matrix H_(est). Each iteration of the recursiveestimation of matrix H_(est) occurs after receiving a corresponding oneof the plurality of training fields.

In other features the receiver module further includes a plurality ofFFT modules that convert the data from time domain signals to frequencydomain signals. Respective outputs of the plurality of FFT modulescommunicate with respective inputs of the equalizer module. The receivermodule includes a Viterbi decoder module that generates data symbolsbased on the frequency domain signals communicated from an output of theequalizer module. The plurality of training fields are compliant withIEEE 802.11n.

In other features a transceiver module includes the receiver module andfurther includes a transmitter module. The transmitter module generatestraining symbols that are to be included in the plurality of trainingfields and includes a multiplier module that multiplies the trainingsymbols by a matrix P. The matrix P has a condition number equal to 1.

A method of operating a receiver includes receiving a data message froma wireless communication channel. The data message has a plurality oftraining fields and data. The method includes recursively estimating amatrix H that represents the channel based on the plurality of trainingfields. The recursive estimating is performed as the plurality oftraining fields are being received. The method also includes applyingcoefficients to the data based on the matrix H.

In other features the recursive estimating step begins upon receiving afirst one of the training fields and finishes upon receiving a final oneof the plurality of training fields. The matrix H is based on a matrix Pand the plurality of training symbols are processed in accordance withthe matrix P prior to being transmitted. The recursive estimation ofmatrix H includes recursively estimating a matrix H_(est) based on theplurality of training fields and estimating matrix H based on an inverseof matrix P and a final value of the matrix H_(est). Each iteration ofthe recursive estimation of matrix H_(est) occurs after receiving acorresponding one of the plurality of training fields.

In other features the method includes converting the data from timedomain signals to frequency domain signals. The method includescommunicating the frequency domain signals to the step of applyingcoefficients. The method includes generating data symbols based onfrequency domain signals that are output from the step of applyingcoefficients. The plurality of training fields are compliant with IEEE802.11 n.

In other features the method is adapted to operating a transceivermodule by including transmitting a wireless signal over the wirelesscommunication channel. The transmitting step includes generatingtraining symbols that are to be included in the plurality of trainingfields and multiplying the training symbols by a matrix P. The matrix Phas a condition number equal to 1.

A receiver module includes input means for receiving a data message froma wireless communication channel. The data message has a plurality oftraining fields and data. Channel estimator means recursively estimate amatrix H that represents the channel based on the plurality of trainingfields. The recursive estimation is performed as the plurality oftraining fields are being received. Equalizer means apply coefficientsto the data based on the matrix H.

In other features the channel estimator means begins the recursiveestimation upon receiving a first one of the training fields andfinishes the recursive estimation upon receiving a final one of theplurality of training fields. The channel estimator means estimates thematrix H based on a matrix P. The plurality of training symbols areprocessed in accordance with the matrix P prior to being transmitted tothe receiver module. The recursive estimation of matrix H includesrecursively estimating a matrix H_(est) based on the plurality oftraining fields and estimating matrix H based on an inverse of matrix Pand a final value of the matrix H_(est). Each iteration of the recursiveestimation of matrix H_(est) occurs after receiving a corresponding oneof the plurality of training fields.

In other features the receiver module includes FFT means for convertingthe data from time domain signals to frequency domain signals.Respective outputs of the FFT means communicate with respective inputsof the equalizer means. The receiver module includes a Viterbi decodermodule that generates data symbols based on frequency domain signalscommunicated from an output of the equalizer module. The plurality oftraining fields are otherwise compliant with IEEE 802.11 n.

In other features a transceiver module includes the receiver and furtherincludes transmitter means for transmitting a wireless signal over thewireless communication channel. The transmitter means generates trainingsymbols that are to be included in the plurality of training fields andincludes multiplier means for multiplying the training symbols by amatrix P. The matrix P has a condition number equal to 1.

In still other features, a computer program executed by a processorassociated with a receiver includes receiving a data message from awireless communication channel. The data message has a plurality oftraining fields and data. The computer program includes recursivelyestimating a matrix H that represents the channel based on the pluralityof training fields. The recursive estimating is performed as theplurality of training fields are being received. The computer programalso includes applying coefficients to the data based on the matrix H.

In other features the recursive estimating step begins upon receiving afirst one of the training fields and finishes upon receiving a final oneof the plurality of training fields. The matrix H is based on a matrix Pand the plurality of training symbols are processed in accordance withthe matrix P prior to being transmitted. The recursive estimation ofmatrix H includes recursively estimating a matrix H_(est) based on theplurality of training fields and estimating matrix H based on an inverseof matrix P and a final value of the matrix H_(est). Each iteration ofthe recursive estimation of matrix H_(est) occurs after receiving acorresponding one of the plurality of training fields.

In other features the computer program includes converting the data fromtime domain signals to frequency domain signals. The computer programincludes communicating the frequency domain signals to the step ofapplying coefficients. The computer program includes generating datasymbols based on frequency domain signals that are output from the stepof applying coefficients. The plurality of training fields are compliantwith IEEE 802.11n.

In other features the computer program is adapted to operating atransceiver module by including transmitting a wireless signal over thewireless communication channel. The transmitting step includesgenerating training symbols that are to be included in the plurality oftraining fields and multiplying the training symbols by a matrix P. Thematrix P has a condition number equal to 1.

In still other features, the systems and methods described above areimplemented by a computer program executed by one or more processors.The computer program can reside on a computer readable medium such asbut not limited to memory, non-volatile data storage and/or othersuitable tangible storage mediums.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating the preferred embodiment of the disclosure, are intended forpurposes of illustration only and are not intended to limit the scope ofthe disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of a multiple input, multipleoutput (MIMO) communication system according to the prior art;

FIG. 2 is a functional block diagram of a MIMO communication system thatincludes a receiver that employs a recursive channel estimation method;

FIG. 3 is a functional block diagram of a MIMO transceiver that includesthe receiver of FIG. 2;

FIG. 4 is a data diagram of a prior art data message that is transmittedby a transmitter module of the communication system of FIG. 2;

FIG. 5 is a flowchart of the recursive channel estimation method;

FIG. 6A is a functional block diagram of a high definition television;

FIG. 6B is a functional block diagram of a vehicle control system;

FIG. 6C is a functional block diagram of a cellular phone;

FIG. 6D is a functional block diagram of a set top box; and

FIG. 6E is a functional block diagram of a media player.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is in no wayintended to limit the disclosure, its application, or uses. For purposesof clarity, the same reference numbers will be used in the drawings toidentify similar elements. As used herein, the term module, circuitand/or device refers to an Application Specific Integrated Circuit(ASIC), an electronic circuit, a processor (shared, dedicated, or group)and memory that execute one or more software or firmware programs, acombinational logic circuit, and/or other suitable components thatprovide the described functionality. As used herein, the phrase at leastone of A, B, and C should be construed to mean a logical (A or B or C),using a non-exclusive logical or. It should be understood that stepswithin a method may be executed in different order without altering theprinciples of the present disclosure.

Referring now to FIG. 2, a functional block diagram is shown of a MIMOcommunication system 50. Communication system 50 includes a receivermodule 52 that employs a recursive channel estimation method (shown inFIG. 5). The recursive channel estimation method estimates conditions ina wireless communication channel 54. The recursive estimation methodbegins with a first long training sequence that is sent by a transmittermodule 56. The recursive estimation method ends by generating a channelestimation matrix H when the last long training sequence has beenreceived. Since the recursive estimation method develops a basis forgenerating matrix H while the long training sequences are beingreceived, instead of starting after the long training sequences havebeen received, the recursive estimation method can generate matrix Hfaster than previously known methods. The matrix H can then be used toperform channel equalization in receiver module 52 to compensate for theeffects of communication channel 54.

Communication system 50 will now be described in pertinent part. Abaseband module 58 generates data messages based on m streams ofincoming data. Baseband module 58 communicates the data messages (shownin FIG. 4) to an encoder module 60. The data messages include respectivelong training fields that are compliant with IEEE 802.11n. Encodermodule 60 encodes the long training fields into n data streams based onthe matrix P, which is shown in FIG. 1. Encoder module 60 communicatesthe n data streams to n respective transmit channels 62-1, . . . , 62-n,which are referred to collectively as transmit channels 62. Eachtransmit channel 62 includes a respective modulation module 64 thatmodulates its respective data stream, such as with quadrature-amplitudemodulation (QAM), and communicates the modulated data stream to arespective inverse fast-Fourier transform (IFFT) module 66. IFFT modules66 convert their respective data streams from a frequency domain signalto a time domain signal. IFFT modules 66 communicate the time domainsignals to respective radio frequency (RF) transmitters that arerepresented by antennas 68.

The transmitted data streams propagate through communication channel 54.Communication channel 54 perturbs the transmitted data streams due tophenomena such as reflections, signal attenuation, and so forth. Theperturbations can be represented by matrix H.

Receiver module 52 includes n RF receivers that are represented byantennas 70-1, . . . , 70-n. The RF receivers receive the transmitteddata streams and communicate the perturbed time domain signals to achannel estimator module 72. Channel estimator module 72 estimatesmatrix H based on matrix P and the long training fields that areincluded in the received data streams. In some embodiments channelestimator module 72 includes a processor 73 and associated memory 75 forstoring and/or executing the recursive channel estimation methods thatare described below.

Channel estimator module 72 communicates the n received data streams ton respective fast-Fourier transform (FFT) modules 74 and adjusts gainsof an equalizer module 76. FFT modules 74 convert the time-domain datastreams to frequency-domain data streams and communicate them toequalizer module 76. Equalizer module 76 compensates the respective datastreams based on the gains and communicates the compensated gains to aViterbi decoder module 78. Viterbi decoder module 78 decodes the n datastreams to generate received data streams y_(m).

Referring now to FIG. 3, a functional block diagram is shown of atransceiver 80 that includes transmitter module 56 and receiver module52. Transceiver 80 can communicate with other transceivers 80 viaantennas 82-1, . . . 82-n. An antennas switch module 84 selectivelyconnects antennas 82 to transmitter module 56 or receiver module 52based on whether transceiver 80 is transmitting or receiving.

Referring now to FIG. 4, a data diagram is shown of an IEEE 802.11n datamessage 90. Data message 90 includes data 92 and a preamble 94 thatcontains a plurality of training fields. Preamble 94 is divided into afirst portion 96 and a second portion 98. First portion 96 may be usedby legacy systems, e.g. non-MIMO, IEEE 802.11 communication systems.Second portion 98 includes a signal filed field 100, a short trainingfield 102, and x long training fields (LTFs) 104-1, . . . , 104-x, wherex is an integer. Each LTF 104 includes k training symbols 106 or tones.Short training field 102 is generally used by receiver module 52 toestablish symbol timing of data message 90. Channel estimator module 72uses LTFs 104 and their k respective training symbols 106 to estimatematrix H based on methods that are described below.

Referring now to FIG. 5, a method 120 is shown for estimating matrix H.Method 120 can be executed by channel estimator module 72. In someembodiments method 120 can be implemented as a computer program orfirmware that is stored in memory 75 and executed by processor 73.

Control enters at a block 122 and proceeds to decision block 124. Indecision block 124 control determines whether an LTF 104 is beingreceived. If not then control returns to block 122. If an LTF 104 isbeing received then control branches from decision block 124 to block126. In block 126 control receives a training symbol 106 that isassociated with the current LTF 104. Control then proceeds to block 128and updates a matrix H_(est), which is described below in more detail,based on the current training symbol 106. Control then proceeds todecision block 130 and determines whether the current training symbol106 was the last training symbol 106 of the present LTF 104. If not thencontrol branches to block 132 and waits for the next training symbol 106of the current LTF 104. When the next training symbol 106 is receivedcontrol returns to block 126 and repeats the aforementioned steps forthe new training symbol 106. On the other hand, if the training symbol106 in decision block 130 was the last training symbol 106 of thepresent LTF 104 then control branches to decision block 134.

In decision block 134 control determines whether the current LTF 104 wasthe last LTF 104 (i.e. LTF 104-x) of the current group of LTFs 104. Ifnot then control branches to block 136 and waits for the next LTF 104 tobegin before returning to block 126. On the other hand, if the currentLTF 104 was the last LTF 104-x then control branches from decision block134 to block 138. In block 138 control generates matrix H based onmatrix H_(est) and matrix P. Control then proceeds to block 140 andadjusts the gains of equalizer module 76 based on matrix H. Control thenreturns to other processes via termination block 142.

As channel estimator module 72 executes method 120 it performsdistributed QR across LTFs 104. That is, QR(H_(est)). Computationaldensity therefore increases as O(n²) and the processing latency ofassociated hardware and/or processor 73 would increase by about O(n²).This represents an improvement, e.g. reduced need for processing power,over the prior art. Example estimations of matrix H_(est) will now beprovided for various MIMO dimensions of communications system 50.

2×2 And 2×3 Mimo Cases

In 2×2 and 2×3 MIMO cases the equalized vector is given by

$\hat{x} = {\frac{1}{{diag}\left( {P_{2 \times 2}R_{2 \times 2}^{- 1}R_{2 \times 2}^{-^{*}}P_{2 \times 2}^{T}} \right)}P_{2 \times 2}R_{2 \times 2}^{- 1}Q^{*}y}$

It can be seen that

${\hat{x} = {{{\begin{bmatrix}\frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} + r_{12}}}^{2}} & 0 \\0 & \frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} - r_{12}}}^{2}}\end{bmatrix}\begin{bmatrix}1 & {- 1} \\1 & 1\end{bmatrix}}\begin{bmatrix}\frac{1}{r_{11}} & {- \frac{r_{12}}{r_{11}r_{22}}} \\0 & \frac{1}{r_{22}}\end{bmatrix}}Q^{*}y}},{where}$ ${W_{} = \begin{bmatrix}\frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} + r_{12}}}^{2}} & 0 \\0 & \frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} - r_{12}}}^{2}}\end{bmatrix}},{P_{2 \times 2} = \begin{bmatrix}1 & {- 1} \\1 & 1\end{bmatrix}},{and}$ $R_{2 \times 2}^{- 1} = {\begin{bmatrix}\frac{1}{r_{11}} & {- \frac{r_{12}}{r_{11}r_{22}}} \\0 & \frac{1}{r_{22}}\end{bmatrix}.}$

4×4 Spatial-Multiplexing (SM) Mimo Case

For a general n×n MIMO communication system 50 the equalized vector isgiven by

${\hat{x}}_{n} = {\frac{1}{{diag}\left( {P_{n}R_{n}^{- 1}R_{n}^{-^{*}}P_{n}^{T}} \right)}P_{n}R_{n}^{- 1}Q_{n}^{*}y}$where H_(est, n) = Q_(n)R_(n).

Methods are known in the art for recursively solving the Q*_(n)y term ofthe above equation. Recursive computation of the P_(n)R_(n) ⁻¹ and

$\underset{\_}{w_{{ll},n}} = {1./{{diag}\left( {P_{n}R_{n}^{- 1}R_{n}^{- *}P_{n}^{T}} \right)}}$

terms of the above equation will now be described.

4×4 SM Mimo Case—Substream Signal-to Noise Ratio (SNR) Recursion

Let w _(∥,n)=1./diag(P_(n×n)R_(n×n) ⁻¹R_(n×n) ⁻*P_(n×n) ^(T)). It can beseen that for 1≦j<n the j^(th) element of the w_(∥) vector for n streamscan be recursively computed as follows:

$\frac{1}{w_{{ll},n}^{j}} = {\frac{1}{w_{{ll},{n - 1}}^{j}} + k_{j}}$where${k_{j} = \left( {P_{n \times n}\underset{\_}{v}{\underset{\_}{v}}^{*}P_{n \times n}^{T}} \right)_{jj}},{R_{n \times n}^{- 1} = {{{\left\lbrack {\begin{matrix}R_{n - {1 \times n} - 1}^{- 1} \\{\; \underset{\_}{0}}\end{matrix}\underset{\_}{v}} \right\rbrack.{For}}\mspace{14mu} j} = n}},{w_{{ll},n}^{n} = \frac{1}{\lambda_{n} + k_{n}}}$whereλ_(n) = P(n, 1:n − 1)R_(n − 1)⁻¹R_(n − 1)^(−^(*))P(n, 1:n − 1)^(T).

A proof of the immediately preceding equations will now be provided.

$R_{n \times n}^{- 1} = \left\lbrack {\begin{matrix}R_{n - {1 \times n} - 1}^{- 1} \\{\; \underset{\_}{0}}\end{matrix}\underset{\_}{v}} \right\rbrack$ $\begin{matrix}{{{diag}\left( {P_{n \times n}R_{n \times n}^{- 1}R_{n \times n}^{-^{*}}P_{n \times n}^{T}} \right)} = {{diag}\left( {{{P_{n}\left\lbrack {\begin{matrix}R_{n - 1}^{- 1} \\{\; \underset{\_}{0}}\end{matrix}\underset{\_}{v}} \right\rbrack}\left\lbrack {\begin{matrix}R_{n - 1}^{- 1} \\{\; \underset{\_}{0}}\end{matrix}\underset{\_}{v}} \right\rbrack}^{*}P_{n}^{T}} \right)}} \\{= {{diag}\left( {{P_{n}\left( {\left\lbrack {\begin{matrix}{R_{n - 1}^{- 1}R_{n - 1}^{-^{*}}} \\{\; \underset{\_}{0}}\end{matrix}\underset{\_}{0}} \right\rbrack + {\underset{\_}{v}{\underset{\_}{v}}^{*}}} \right)}P_{n}^{T}} \right)}} \\{= {{diag}\left( {{P_{n - 1}R_{n - 1}^{- 1}R_{n - 1}^{-^{*}}P_{n - 1}^{T}},P_{({n,{{1\text{:}n} - 1}})}} \right.}} \\{\left. {R_{n - 1}^{- 1}R_{n - 1}^{-^{*}}P_{({n,{{1\text{:}n} - 1}})}^{T}} \right) + {{diag}\left( {P_{n}\underset{\_}{v}{\underset{\_}{v}}^{*}P_{n}^{T}} \right)}}\end{matrix}$

4×4 SM Mimo Case—Processing the 2^(nd) LTF 104

${{Compute}\mspace{14mu} {R_{2 \times 2}.{Compute}}\mspace{14mu} {{R_{2 \times 2}^{- 1}\begin{bmatrix}{1/} & {{{- r_{12}}/r_{11}}r_{22}} \\0 & {1/r_{22}}\end{bmatrix}}.{Compute}}\mspace{14mu} {1/w_{{ll},1}}} = {{{\left( {r_{22}^{2} + {{r_{11} + r_{12}}}^{2}} \right)/r_{11}^{2}}{r_{22}^{2}.{Compute}}\mspace{14mu} {1/w_{{ll},2}}} = {{{\left( {r_{22}^{2} + {{r_{11} - r_{12}}}^{2}} \right)/r_{11}^{2}}{r_{22}^{2}.{Let}}\mspace{14mu} \lambda} = {1/{w_{{ll},2}.}}}}$

4×4 SM Mimo Case—Processing the 3^(rd) LTF 104

Update the inverse of the triangular matrix based on

$R_{3 \times 3} = \left\lbrack {\begin{matrix}R_{2 \times 2} \\{\; \underset{\_}{0}}\end{matrix}\left\lbrack {r_{13}\mspace{31mu} r_{23}\mspace{31mu} r_{33}} \right\rbrack}^{T} \right\rbrack$$R_{3 \times 3}^{- 1} = \left\lbrack {\begin{matrix}R_{2 \times 2}^{- 1} \\{\; \underset{\_}{0}}\end{matrix}\left\lbrack {\rho_{1}\mspace{31mu} \rho_{2}\mspace{31mu} \rho_{3}} \right\rbrack}^{T} \right\rbrack$

where ρ₁=(r ₁₂ r ₂₃ −r ₁₃ r ₂₂)/r ₁₁ r ₂₂ r ₃₃ ρ₂₃ −r ₂₃ /r ₂₂ r ₃₃ρ3=−1/r ₃₃.

Update the substream SNRs based on

1/w _(∥,1)→1/w _(∥,1)+∥ρ₁ρ₂+ρ₃∥²

1/w _(∥,2)→1/w _(∥,2)+∥ρ₁+ρ₂−ρ₂∥²

1/w _(∥,3)→λ−∥ρ₁−ρ₂+ρ₃∥².

Update the lamda factor based on

λ=1/w _(∥,1)+1/w _(∥,1)−1/w _(∥,3)+8real(ρ₂)ρ₃.

4×4 SM Mimo Case—Processing the 4^(th) LTF 104

Update the inverse of the triangular matrix based on

$R_{4 \times 4} = \left\lbrack {\begin{matrix}R_{3 \times 3} \\{\; \underset{\_}{0}}\end{matrix}\left\lbrack {r_{14}\mspace{31mu} r_{24}\mspace{31mu} r_{34}\mspace{31mu} r_{44}} \right\rbrack}^{T} \right\rbrack$$R_{4 \times 4} = \left\lbrack {\begin{matrix}R_{3 \times 3} \\{\; \underset{\_}{0}}\end{matrix}\left\lbrack {r_{14}\mspace{31mu} r_{24}\mspace{31mu} r_{34}\mspace{31mu} r_{44}} \right\rbrack}^{T} \right\rbrack$

where

ρ₁=(r ₃₃(r ₁₂ r ₂₄ −r ₁₄ r ₂₂)−(r ₁₂ r ₂₃ −r ₁₃r₂₂)r ₃₄)/r ₁₁ r ₂₂ r ₃₃r ₄₄,

ρ₂=(r ₃₄ r ₂₃ −r ₂₄ r ₃₃)/r ₂₂ r ₃₃ r ₄₄, ρ₃ =−r ₃₃ /r ₃₃ r ₄₄, ρ₄=1/r₄₄

Update the substream SNR based on

1/w _(∥,2)→1/w _(∥,2)+∥ρ₁ρ₂−ρ₃+ρ₄∥²

1/w _(∥,3)→1/w _(∥,3)+∥ρ₁+ρ₂−ρ₃−ρ₄∥²

1/w _(∥,4)→λ+∥−ρ₁+ρ₂+ρ₃+ρ₄∥².

1/w _(∥,4)→λ+∥−ρ₁+ρ₂+ρ₃+ρ₄∥².

Compute their inverses and store them in a memory that can be includedin channel estimator module 72.

3×3 SM Mimo Case—Processing the 4^(th) LTF 104

The 3×3 MIMO case employs a non-square matrix P. For 3 streamstransmitter module 56 sends 4 LTFs 104 and employs matrix P of

$P_{3} = {\begin{bmatrix}1 & {- 1} & 1 & 1 \\1 & 1 & {- 1} & 1 \\1 & 1 & 1 & {- 1}\end{bmatrix}.}$

Channel estimator module 72 estimates channel matrix H_(est3×4) and thereal matrix is H=H_(est3×4)P_(3×4) ^(⊥). The received vector can bebased on y=H_(est3×4)P_(3×4) ^(⊥)x=Hx.

A distributed solution may also be employed by working directly withH_(est3×4) without forming H. In the distributed solution let

H_(est3×4)=QR_(3×4) and

H_(est3×4)=[H_(est3×3)h₄]

Then Q*H_(est3×4)=└R Q*h₄┘ where QR=H_(est3×3).

In some embodiments the equalized vector can be based on

{circumflex over (x)}=(H _(est,3×4) P _(3×4) ^(⊥))^(⊥) y.

It can be seen that

{circumflex over (x)}=P ₁ ⁻¹ z−μv where u=R ⁻¹ Q*h ₄, and μ=[1−1 1] z.

The vector v is based on

v=kP ₁ ⁻¹ u where u=R ⁻¹ Q*h ₄.

The scalar k is based on

k=1/(1+[1−1 1] u ).

The matrix P₁ ⁻¹ is based on

$P_{1}^{- 1} = {{2\begin{bmatrix}1 & {- 1} & 0 \\1 & 0 & {- 1} \\0 & 1 & 1\end{bmatrix}}.}$

A proof of the immediately preceding equations will now be provided.

A solution is given by {circumflex over (x)}=(H_(est,3×4)P_(3×4)^(⊥))⁻¹y.

Let

$P_{3 \times 4}^{\bot} = \begin{bmatrix}P_{1} \\P_{2}\end{bmatrix}$

and write the matrix as

$\begin{matrix}{\left( {H_{{est},{3 \times 4}}P_{3 \times 4}^{\bot}} \right)^{- 1} = \left\lbrack {{H_{{est},{3 \times 3}}P_{1}} + {h_{4}p_{1}}} \right\rbrack^{- 1}} \\{= \left\lbrack {{QRP}_{1} + {h_{4}p_{1}}} \right\rbrack^{- 1}} \\{= {{P_{1}^{- 1}R^{- 1}Q^{*}} - \frac{P_{1}^{- 1}R^{- 1}Q^{*}h_{4}p_{1}P_{1}^{- 1}R^{- 1}Q^{*}}{1 + {p_{1}P_{1}^{- 1}R^{- 1}Q^{*}h_{4}}}}} \\{= {\left\lbrack {I - \frac{{vp}_{1}}{1 + {p_{1}v}}} \right\rbrack P_{1}^{- 1}R^{- 1}Q^{*}}}\end{matrix}$

where v=P₁ ⁻¹R⁻¹Q*h₄.

${P_{1}^{- 1} = {2\begin{bmatrix}1 & {- 1} & 0 \\1 & 0 & {- 1} \\0 & 1 & 1\end{bmatrix}}},{{p_{1}P_{1}^{- 1}} = {\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack.}}$

3×3 SM Mimo Case—Solution for W_(∥)

Channel estimator module 72 computes

W _(∥)=1((H _(est,3×4) P _(3×4) ^(⊥))*(H _(est,3×4) P _(3×4) ^(⊥)))⁻¹

based on terms of v=k P₁ ⁻¹R⁻¹Q*h₄ and R⁻¹R⁻*.

Let this matrix be

${R^{- 1}R^{-^{*}}} = \begin{bmatrix}{I_{11} + {j\; Q_{11}}} & {I_{21} - {j\; Q_{21}}} & {I_{31} - {j\; Q_{31}}} \\{I_{21} + {j\; Q_{21}}} & {I_{22} + {j\; Q_{22}}} & {I_{32} - {j\; Q_{32}}} \\{I_{31} + {j\; Q_{31}}} & {I_{32} + {j\; Q_{32}}} & {I_{33} + {j\; Q_{33}}}\end{bmatrix}$

and during LTFs 104 compute

S ₁=4(I ₁₁−2I ₂₁ +I ₂₂)

S ₂=4(I ₁₁−2I ₃₁ +I ₃₃)

S ₃=4(I ₂₂+2I ₃₂ +I ₃₃)

S=(I ₁₁ +I ₂₂ +I ₃₃)−2(I ₂₁ +I−I ₃₂)

S ₄ =I ₁₁−2I ₂₁ +I ₂₂ −I ₃₁ +I ₃₂ +j(Q ₁₁ +Q ₂₂ +Q ₃₁ −Q ₃₂)

S ₅ =I ₁₁ −I ₂₁ +I ₃₂−2I ₃₁ +I ₃₃ +j(Q ₁₁ +Q ₂₁ +Q ₃₂ +Q ₃₃)

S ₆ =I ₂₁ −I ₂₂ +I ₃₁−2I ₃₂ −I ₃₃ +j(Q ₂₁ −Q ₂₂ +Q ₃₁ −Q ₃₂)

It can be seen that

W _(∥1)=1/(S ₁ +S∥v ₁∥²−4real(S ₄v₁*))

W _(∥2)=1/(S ₂ +S∥v ₂∥²−4real(S ₅v₂*))

W _(∥3)=1/(S ₃ +S∥v ₃∥²−4real(S ₆ v ₃*))

and v=kP₁ ⁻ u.

Proof of the above solution for W_(∥) will now be provided. Let

H=[QR h ₄ ]P _(3×) ^(⊥)

Q*H=└R Q*h ₄ ┘P _(3×4) ^(⊥) =R(P ₁ +up ₁), u=R ⁻¹ Q*h ₄

Then

$\begin{matrix}{\left( {H^{*}H} \right)^{- 1} = {\left( {P_{1} + {\underset{\_}{u}p_{1}}} \right)^{- 1}R^{- 1}{R^{-^{*}}\left( {P_{1}^{T} + {p_{1}^{T}{\underset{\_}{u}}^{*}}} \right)}^{- 1}}} \\{= {\left( {I - \frac{P_{1}^{- 1}\underset{\_}{u}p_{1}}{1 + {\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack \underset{\_}{u}}}} \right)P_{1}^{- 1}R^{- 1}R^{-^{*}}P_{1}^{- T}}} \\{\left( {I - \frac{p_{1}^{T}{\underset{\_}{u}}^{*}P_{1}^{- T}}{1 + {\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack \underset{\_}{u}}}} \right)} \\{= {\left( {P_{1}^{- 1} - {v\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack}} \right)R^{- 1}R^{-^{*}}}} \\{\left( {P_{1}^{- T} - {\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack^{T}v^{*}}} \right)} \\{= {{P_{1}^{- 1}R^{- 1}R^{-^{*}}P_{1}^{- T}} + {{v\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack}R^{- 1}R^{-^{*}}}}} \\{{{\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack^{T}v^{*}} - {2\mspace{14mu} {real}\mspace{11mu} \left( {P_{1}^{- 1}R^{- 1}R^{-^{*}}} \right.}}} \\\left. {\left\lbrack {1\mspace{31mu} - 1\mspace{31mu} - 1} \right\rbrack v^{*}} \right)\end{matrix}$ v = kP₁⁻¹R⁻¹Q^(*)h₄.

Channel estimator module 72 still needs to recursively update R⁻¹R⁻*after determining v=kP₁ ⁻¹ u as described above. At a time n let

R _(n) ⁻¹ =[R _(n−1) ⁻¹ρ]

and apply the following identity

R _(n) ⁻¹ R _(n) ⁻ *=R _(n−1) ⁻¹ R _(n−1) ⁻*+ρρ*.

For example,

$R_{3 \times 3}^{- 1} = \left\lbrack {\begin{matrix}R_{2 \times 2}^{- 1} \\\underset{\_}{0}\end{matrix}\begin{bmatrix}\rho_{1} & \rho_{2} & \rho_{3}\end{bmatrix}}^{T} \right\rbrack$ ρ₁ = (r₁₂r₂₃ − r₁₃r₂₂)/r₁₁r₂₂r₃₃ρ₂₌ − r₂₃/r₂₂r₂₃ ρ₃₌1/r₃₃.

3×3 SM Mimo Case—Processing the 1^(st) LTF 104

Channel estimator module 72 performs first column nulling by computing

R ₁ ⁻¹=1/r₁₁.

3×3 SM Mimo Case—Processing the 2^(nd) LTF 104

Channel estimator module 72 performs second column QR processing basedon

${R_{2 \times 2}^{- 1} = {{\left\lbrack {\begin{matrix}R_{1}^{- 1} \\\underset{\_}{0}\end{matrix}\begin{bmatrix}\rho_{1} & \rho_{2}\end{bmatrix}}^{T} \right\rbrack \mspace{14mu} {where}\mspace{14mu} \rho_{1}} = {{{- r_{12}}/r_{11}}r_{22}}}},{{{and}\mspace{14mu} \rho_{2}} = {1/{r_{22}.}}}$

Channel estimator module 72 then computes μρ₁∥², ∥ρ₂∥², ρ₁ρ₂* andupdates R⁻¹R⁻* based on

${R_{2 \times 2}^{- 1}R_{2 \times 2}^{-^{*}}} = {\begin{bmatrix}{{1/r_{11}} + {\rho_{1}}^{2}} & {\rho_{1}\rho_{2}^{*}} \\{\rho_{1}^{*}\rho_{2}} & {\rho_{2}}^{2}\end{bmatrix}.}$

3×3 SM Mimo Case—Processing the 3^(rd) LTF 104

Channel estimator module 72 performs third column QR processing byrecursively updating

$R_{3 \times 3}^{- 1} = \left\lbrack {\begin{matrix}R_{2 \times 2}^{- 1} \\\underset{\_}{0}\end{matrix}\begin{bmatrix}\rho_{1} & \rho_{2} & \rho_{3}\end{bmatrix}}^{T} \right\rbrack$

where ρ₁=(r₁₂r₂₃−r₁₃r₂₂)/r₁₁r₂₂r₃₃ ρ₂=−r₂₃/r₂₂r₃₃ ρ₃=1/r₃₃.

Channel estimator module 72 can then compute

∥ρ₁∥², ∥ρ₂∥², ρ₂∥², ρ₁ρ₂*, ρ₁ρ₃*, ρ₂ρ₃*

and update R⁻¹R⁻* based on

R _(3×3) ⁻¹ R _(3×3) ⁻ *=R _(2×2) ⁻¹ R _(2×2) ⁻*+ρρ*.

Channel estimator module 72 can then compute the sums

S ₁=4(I ₁₁−2I ₂₁ +I ₂₂)

S ₂=4(I ₁₁−2I ₃₁ +I ₃₃)

S ₃=4(I ₂₂+2I ₃₂ +I ₃₃)

S=(I ₁₁ +I ₂₂ +I ₃₃)−2(I ₂₁ +I−I ₃₂)

S ₄ =I ₁₁−2I ₂₁ +I ₂₂ −I ₃₁ +I ₃₂ +j(Q ₁₁ +Q ₂₂ +Q ₃₁ −Q ₃₂)

S ₅ =I ₁₁ −I ₂₁ +I ₃₂−2I ₃₁ +I ₃₃ +j(Q ₁₁ +Q ₂₁ +Q ₃₂ +Q ₃₃)

S ₆ =I ₂₁ +I ₂₂ +I ₃₁−2I ₃₂ −I ₃₃ +j(Q ₂₁ −Q ₂₂ +Q ₃₁ −Q ₃₂)

3×3 SM Mimo Case—Processing the 4^(th) LTF 104

Channel estimator module 72 computes

u=R ^(−1Q*h) ₄,

k=1/(1+[1−1]u ), and

v=kP ₁ ^(−u.)

Channel estimator module can store v in memory 75.

Channel estimator module 72 computes substream SNR based on

W _(∥1)=1/(S ₁ +S∥v ₁∥²−4 4real(S ₄ v ₁*))

W _(∥2)=1/(S ₂ +A∥v ₂∥²−4real(S ₅ v ₂*))

W _(∥3)=1/(S ₃ +S∥v ₃∥²−4real(S ₆ v ₃*))

and store the substream SNR in memory 75.

3×3 SM Mimo Case—Processing Data 92

Channel estimator module 72 can compute

z=R ⁻¹ Q*y and μ=[1−1 1] z

and read v from memory 75. Channel estimator module 72 can then compute

{circumflex over (x)}=P ₁ ⁻ z−μv

and read the substream SNR from memory 75. Equalizer module 76 can scalethe equalized vector based on the SNRs.

Referring now to FIGS. 6A-6E, various exemplary implementations of thereceiver module are shown. Referring now to FIG. 6A, the receiver modulecan be implemented in a high definition television (HDTV) 420. Thereceiver module may implement and/or be implemented in a WLAN interface429. The HDTV 420 receives HDTV input signals in either a wired orwireless format and generates HDTV output signals for a display 426. Insome implementations, signal processing circuit and/or control circuit422 and/or other circuits (not shown) of the HDTV 420 may process data,perform coding and/or encryption, perform calculations, format dataand/or perform any other type of HDTV processing that may be required.

The HDTV 420 may communicate with mass data storage 427 that stores datain a nonvolatile manner such as optical and/or magnetic storage devices.Mass data storage 427 may include at least one hard disk drive (HDD)and/or at least one digital versatile disk (DVD) drive. The HDD may be amini HDD that includes one or more platters having a diameter that issmaller than approximately 1.8″. The HDTV 420 may be connected to memory428 such as RAM, ROM, low latency nonvolatile memory such as flashmemory and/or other suitable electronic data storage. The HDTV 420 alsomay support connections with a WLAN via WLAN network interface 429. TheHDTV 420 also includes a power supply 423.

Referring now to FIG. 6B, the receiver module may implement and/or beimplemented in a WLAN interface 448 of a vehicle 430. In someimplementations WLAN interface 448 communicates with a powertraincontrol system 432 that receives inputs from one or more sensors.Examples of sensors includes temperature sensors, pressure sensors,rotational sensors, airflow sensors and/or any other suitable sensorsand/or that generates one or more output control signals such as engineoperating parameters, transmission operating parameters, and/or othercontrol signals.

The receiver module may also be implemented in other control systems 440of the vehicle 430. The control system 440 may likewise receive signalsfrom input sensors 442 and/or output control signals to one or moreoutput devices 444. In some implementations, the control system 440 maybe part of an anti-lock braking system (ABS), a navigation system, atelematics system, a vehicle telematics system, a lane departure system,an adaptive cruise control system, a vehicle entertainment system suchas a stereo, DVD, compact disc and the like. Still other implementationsare contemplated.

The powertrain control system 432 may communicate with mass data storage446 that stores data in a nonvolatile manner. Mass data storage 446 mayinclude at least one HDD and/or at least one DVD drive. The HDD may be amini HDD that includes one or more platters having a diameter that issmaller than approximately 1.8″. The powertrain control system 432 maybe connected to memory 447 such as RAM, ROM, low latency nonvolatilememory such as flash memory and/or other suitable electronic datastorage. The powertrain control system 432 also may support connectionswith a WLAN via a WLAN network interface 448. The control system 440 mayalso include mass data storage, memory and/or a WLAN interface (all notshown). Vehicle 430 may also include a power supply 433.

Referring now to FIG. 6C, the receiver module can be implemented in acellular phone 450 that may include a cellular antenna 451. The receivermodule may implement and/or be implemented in a WLAN interface 468. Insome implementations, the cellular phone 450 includes a microphone 456,an audio output 458 such as a speaker and/or audio output jack, adisplay 460 and/or an input device 462 such as a keypad, pointingdevice, voice actuation and/or other input device. The signal processingand/or control circuits 452 and/or other circuits (not shown) in thecellular phone 450 may process data, perform coding and/or encryption,perform calculations, format data and/or perform other cellular phonefunctions.

The cellular phone 450 may communicate with mass data storage 464 thatstores data in a nonvolatile manner. Mass data storage 450 may includeat least one HDD and/or at least one DVD drive. The HDD may be a miniHDD that includes one or more platters having a diameter that is smallerthan approximately 1.8″. The cellular phone 450 may be connected tomemory 466 such as RAM, ROM, low latency nonvolatile memory such asflash memory and/or other suitable electronic data storage. The cellularphone 450 also may support connections with a WLAN via the WLAN networkinterface 468. The cellular phone 450 may also include a power supply453.

Referring now to FIG. 6D, the receiver module can be implemented in aset top box 480. The receiver module may implement and/or be implementedin a WLAN interface 496. The set top box 480 receives signals from asource such as a broadband source and outputs standard and/or highdefinition audio/video signals suitable for a display 488 such as atelevision and/or monitor and/or other video and/or audio outputdevices. The signal processing and/or control circuits 484 and/or othercircuits (not shown) of the set top box 480 may process data, performcoding and/or encryption, perform calculations, format data and/orperform any other set top box function.

The set top box 480 may communicate with mass data storage 490 thatstores data in a nonvolatile manner. Mass data storage 490 may includeat least one HDD and/or at least one DVD drive. The HDD may be a miniHDD that includes one or more platters having a diameter that is smallerthan approximately 1.8″. The set top box 480 may be connected to memory494 such as RAM, ROM, low latency nonvolatile memory such as flashmemory and/or other suitable electronic data storage. The set top box480 also may support connections with a WLAN via the WLAN networkinterface 496. The set top box 480 may include a power supply 483.

Referring now to FIG. 6E, the receiver module can be implemented in amedia player 500. The receiver module may implement and/or beimplemented in a WLAN interface 516. In some implementations, the mediaplayer 500 includes a display 507 and/or a user input 508 such as akeypad, touchpad and the like. In some implementations, the media player500 may employ a graphical user interface (GUI) that typically employsmenus, drop down menus, icons and/or a point-and-click interface via thedisplay 507 and/or user input 508. The media player 500 further includesan audio output 509 such as a speaker and/or audio output jack. Thesignal processing and/or control circuits 504 and/or other circuits (notshown) of the media player 500 may process data, perform coding and/orencryption, perform calculations, format data and/or perform any othermedia player function.

The media player 500 may communicate with mass data storage 510 thatstores data such as compressed audio and/or video content in anonvolatile manner. In some implementations, the compressed audio filesinclude files that are compliant with MP3 format or other suitablecompressed audio and/or video formats. Mass data storage 510 may includeat least one HDD and/or at least one DVD drive. The HDD may be a miniHDD that includes one or more platters having a diameter that is smallerthan approximately 1.8″. The media player 500 may be connected to memory514 such as RAM, ROM, low latency nonvolatile memory such as flashmemory and/or other suitable electronic data storage. The media player500 also may support connections with a WLAN via the WLAN networkinterface 516. The media player 500 may also include a power supply 513.Still other implementations in addition to those described above arecontemplated.

Those skilled in the art can now appreciate from the foregoingdescription that the broad teachings of the disclosure can beimplemented in a variety of forms. Therefore, while this disclosureincludes particular examples, the true scope of the disclosure shouldnot be so limited since other modifications will become apparent to theskilled practitioner upon a study of the drawings, the specification andthe following claims.

1. A receiver module comprising: an input that receives a data messagefrom a wireless communication channel, the data message having aplurality of training fields and data; a channel estimator module thatrecursively estimates a matrix H that represents the channel based onthe plurality of training fields, the recursive estimation beingperformed as the plurality of training fields are being received; and anequalizer module that applies coefficients to the data based on thematrix H.
 2. The receiver module of claim 1 wherein the channelestimator module begins the recursive estimation upon receiving a firstone of the training fields and finishes the recursive estimation uponreceiving a final one of the plurality of training fields.
 3. Thereceiver module of claim 1 wherein the channel estimator moduleestimates the matrix H based on a matrix P, wherein the plurality oftraining symbols are processed in accordance with the matrix P prior tobeing transmitted to the receiver module.
 4. The receiver module ofclaim 3 wherein the recursive estimation of matrix H includesrecursively estimating a matrix H_(est) based on the plurality oftraining fields and estimating matrix H based on an inverse of matrix Pand a final value of the matrix H_(est).
 5. The receiver module of claim4 wherein each iteration of the recursive estimation of matrix H_(est)occurs after receiving a corresponding one of the plurality of trainingfields.
 6. The receiver module of claim 1 further comprising a pluralityof FFT modules that convert the data from time domain signals tofrequency domain signals.
 7. The receiver module of claim 6 whereinrespective outputs of the plurality of FFT modules communicate withrespective inputs of the equalizer module.
 8. The receiver module ofclaim 7 further comprising a Viterbi decoder module that generates datasymbols based on the frequency domain signals communicated from anoutput of the equalizer module.
 9. The receiver module of claim 1wherein the plurality of training fields are compliant with IEEE802.11n.
 10. A transceiver module comprising the receiver module ofclaim 1 and further comprising a transmitter module.
 11. The transceivermodule of claim 10 wherein the transmitter module generates trainingsymbols that are to be included in the plurality of training fields andincludes a multiplier module that multiplies the training symbols by amatrix P, wherein the matrix P has a condition number equal to
 1. 12. Amethod of operating a receiver, comprising: receiving a data messagefrom a wireless communication channel, the data message having aplurality of training fields and data; recursively estimating a matrix Hthat represents the channel based on the plurality of training fields,the recursive estimating being performed as the plurality of trainingfields are being received; and applying coefficients to the data basedon the matrix H.
 13. The method module of claim 12 wherein the recursiveestimating step begins upon receiving a first one of the training fieldsand finishes upon receiving a final one of the plurality of trainingfields.
 14. The method of claim 12 wherein the matrix H is based on amatrix P and the plurality of training symbols are processed inaccordance with the matrix P prior to being transmitted.
 15. The methodof claim 14 wherein the recursive estimation of matrix H includesrecursively estimating a matrix H_(est) based on the plurality oftraining fields and estimating matrix H based on an inverse of matrix Pand a final value of the matrix H_(est).
 16. The method of claim 15wherein each iteration of the recursive estimation of matrix H_(est)occurs after receiving a corresponding one of the plurality of trainingfields.
 17. The method of claim 12 further comprising converting thedata from time domain signals to frequency domain signals.
 18. Themethod of claim 17 further comprising communicating the frequency domainsignals to the step of applying coefficients.
 19. The method of claim 18further comprising generating data symbols based on frequency domainsignals that are output from the step of applying coefficients.
 20. Themethod of claim 12 wherein the plurality of training fields arecompliant with IEEE 802.11 n.
 21. A method of operating a transceivermodule, comprising the method of claim 12 and further comprisingtransmitting a wireless signal over the wireless communication channel.22. The transceiver module of claim 21 wherein the transmitting stepincludes generating training symbols that are to be included in theplurality of training fields and multiplying the training symbols by amatrix P, wherein the matrix P has a condition number equal to
 1. 23. Areceiver module comprising: input means for receiving a data messagefrom a wireless communication channel, the data message having aplurality of training fields and data; channel estimator means forrecursively estimating a matrix H that represents the channel based onthe plurality of training fields, the recursive estimation beingperformed as the plurality of training fields are being received; andequalizer means for applying coefficients to the data based on thematrix H.
 24. The receiver module of claim 23 wherein the channelestimator means begins the recursive estimation upon receiving a firstone of the training fields and finishes the recursive estimation uponreceiving a final one of the plurality of training fields.
 25. Thereceiver module of claim 23 wherein the channel estimator meansestimates the matrix H based on a matrix P, wherein the plurality oftraining symbols are processed in accordance with the matrix P prior tobeing transmitted to the receiver module.
 26. The receiver module ofclaim 25 wherein the recursive estimation of matrix H includesrecursively estimating a matrix H_(est) based on the plurality oftraining fields and estimating matrix H based on an inverse of matrix Pand a final value of the matrix H_(est).
 27. The receiver module ofclaim 26 wherein each iteration of the recursive estimation of matrixH_(est) occurs after receiving a corresponding one of the plurality oftraining fields.
 28. The receiver module of claim 23 further comprisingFFT means for converting the data from time domain signals to frequencydomain signals.
 29. The receiver module of claim 28 wherein respectiveoutputs of the FFT means communicate with respective inputs of theequalizer means.
 30. The receiver module of claim 29 further comprisinga Viterbi decoder module that generates data symbols based on thefrequency domain signals communicated from an output of the equalizermodule.
 31. The receiver module of claim 23 wherein the plurality oftraining fields are otherwise compliant with IEEE 802.11n.
 32. Atransceiver module comprising the receiver module of claim 23 andfurther comprising a transmitter means for transmitting a wirelesssignal over the wireless communication channel.
 33. The transceivermodule of claim 32 wherein the transmitter means generates trainingsymbols that are to be included in the plurality of training fields andincludes multiplier means for multiplying the training symbols by amatrix P, wherein the matrix P has a condition number equal to 1.